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Wild problems in the theory of representations of $*$-algebras given by generators and relations. (English) Zbl 0939.16010
The authors consider the representations of the $*$-algebra with the generators ${a}_{k},{a}_{k}^{*}$, $k=1,...,n$ which satisfy the polynomial relations ${P}_{j}\left({a}_{1},...,{a}_{n},{a}_{1}^{*},\cdots ,{a}_{n}^{*}\right)=0$, $j=1,\cdots ,m$. Connections between the factor-wild $*$-algebras (NGCR, in other terms) and the pair-wild $*$-algebras are investigated. It is shown that a pair-wild $*$-algebra is a factor-wild $*$-algebra, but the converse of this statement is not true.
Reviewer: G.F.Us (Kyïv)
##### MSC:
 16G60 Representation type of noncommutative rings and modules 46K10 Representations of topological algebras with involution 46L35 Classifications of ${C}^{*}$-algebras 16R50 Other kinds of identities of associative rings 16W10 Associative rings with involution, etc.